Dream Land, you appear to be intermixing certification and operational requirements.
The ‘Landing distance’ for certification is defined in FAR/CS 25; this is usually referred to as the un-factored landing distance. This is the ‘dry’ landing distance which the manufacturer establishes as the baseline for landing performance.
The ‘Required landing distance’ comes from the operational regulations (FAR 121 / EU-OPS) which require the operator to use factored distances depending on aircraft type (jet/prop) and the runway surface condition (dry/wet). In the EU there is a separate category for contaminated operations with different baseline standards and operational assumptions.
The central theme of the thread is if the factored distances required for dispatch also apply to the actual landing requirements. The wording of the operational regulations is not particularly clear, but in the EU it appears to be generally accepted that a factored distance based on actual landing conditions should be used.
A basis of this is the intent to achieve a level of safety for landing which is equivalent to that required for dispatch.
In the US, the certification and dispatch requirements are essentially the same, but the safety aspects and landing distance required in a pre-landing assessment are less clear. The advice in the advisory guidance SAFO 06012 (August 2006), is potentially confusing, but essentially requires:- (A) that operators conduct a pre-landing assessment, and (B) the landing distance required is at least 15% over the ‘actual landing distance’.
The ‘Actual landing distance’ is not necessarily the manufacturer’s un-factored distance or the dispatch distance, but some in-between value representing what best distance might be achievable by line crews, e.g. B 737 QRH 'actual distance'. It is not a fully factored distance, and thus even with 15 % margin this distance is probably less than the dispatch distance, and thus has a smaller safety margin.
A related Boeing presentation is here:-
Slippery Runways